How (not) to Build Identity-Based Encryption from Isogenies

Elif Ozbay Gurler; Patrick Struck

Paper 2025/1726

How (not) to Build Identity-Based Encryption from Isogenies

Elif Ozbay Gurler

, TU Darmstadt

Patrick Struck

, Universität Konstanz

Abstract

In this work we show obstacles when constructing identity-based encryption (IBE) from isogenies. We first give a modular description for IBEs, what we call a canonical IBE, that consists of two components: an identity key derivation scheme and a public-key encryption scheme. This allows us to investigate the identity key derivation scheme (where the obstacles are rooted in) in isolation. We present several approaches, showing that they can either not be realized—extracting the secret keys would require to solve the underlying hardness assumption—or result in IBE schemes that are insecure—users can use their secret keys to compute secret keys of other users. Finally, we identify properties for isogeny-based trapdoor functions that one would need in order to overcome the identified obstacles.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. SAC 2025
Keywords: identity-based encryption IBE isogeny-based cryptography post-quantum PQC
Contact author(s): elif oezbay @ tu-darmstadt de
patrick struck @ uni-konstanz de
History: 2025-09-24: revised; 2025-09-22: received; See all versions
Short URL: https://ia.cr/2025/1726
License: CC BY

BibTeX

@misc{cryptoeprint:2025/1726,
      author = {Elif Ozbay Gurler and Patrick Struck},
      title = {How (not) to Build Identity-Based Encryption from Isogenies},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1726},
      year = {2025},
      url = {https://eprint.iacr.org/2025/1726}
}